The IEEE standard 802.11n-2009 is a standard for wireless communications using Orthogonal Frequency Division Multiplexing (OFDM) modulation schemes. Under these schemes an inverse fast Fourier transform (IFFT) is used to modulate information onto equally spaced frequency tones (sub-carriers) contained within a frequency band or channel which has a bandwidth of 40 MHz.
The IEEE standard 802.11n-2009 defines three data packet formats or transmission modes. The first of these formats is a non high throughput (Non-HT) format. The second packet format is a high throughput mixed (HT-MF) format, whilst the third format is a high throughput green field (HT-GF) format. The IEEE standard 802.11n-2009 specifies that a Non-HT wireless station (such as a fixed wireless access point or a mobile telephone, for example) can only transmit and receive non-HT data packets. A high throughput (HT) wireless station can transmit and receive non-HT and HT-MF data packets and optionally HT-GF data packets.
Under the IEEE standard 802.11n-2009 data is transmitted using multiple sub-carriers within 20 MHz channels. For HT wireless stations, the standard optionally permits data transmissions in which two adjacent channels, known as a primary channel and a secondary channel, are combined to form a 40 MHz channel. In the HT-MF and HT-GF modes this increased bandwidth results in a higher data rate for modulations other than the MCS32 modulation and coding scheme, whilst in the non-HT mode the same data is transmitted simultaneously on both channels, with a phase shift being introduced to the data transmitted on one channel with respect to the data transmitted on the other channel, giving rise to a transmission mode known as Non-HT Duplicate Mode. Non-HT wireless stations can only transmit in 20 MHz channels and cannot receive HT-MF and HT-GF transmissions from 40 MHz capable HT stations. A 40 MHz capable HT station can transmit and receive 20 MHz data packets.
It has been found that when data signals modulated using the non-HT duplicate mode modulation scheme are interpolated to a higher sampling rate than usual, for example twice the sampling rate of the data to be transmitted (which is equal to the channel bandwidth of the transmitted signal), the interpolated signals have higher peak-to-mean amplitude ratios than those of normal 40 MHz centred modulation schemes such as the modulation and coding scheme MCS7. The same problem exists for the MCS32 modulation and coding scheme defined in the IEEE standard 802.11n-2009. This is illustrated in the graph of FIG. 1, which shows peak to mean amplitude ratios for the MCS7, MCS32 and Non-HT Duplicate modulation schemes.
A high peak-to-mean amplitude ratio can impose a number of problems for subsequent processing of the signal to be transmitted, such as low efficiency of a power amplifier of the transmitter and high power consumption, wide dynamic range for digital processing and more strict fidelity requirements for analogue circuitry of the transmitter.
The reason for the high peak-to-mean amplitude ratio of duplicate modulation schemes such as MCS32 and non-HT duplicate lies in the signal structure of duplicate mode modulated signals, as will be explained below. A payload symbol of a 20 MHz duplicate mode transmission can be represented as a continuous time signal r20Mdup(t):
                                                                                          r                                      20                    ⁢                                                                                  ⁢                    Mdup                                                  ⁡                                  (                  t                  )                                            =                            ⁢                                                ∑                                      k                    =                                          -                      26                                                        26                                ⁢                                                                  ⁢                                                      S                    k                                    ⁢                                      {                                                                  exp                        ⁡                                                  (                                                                                    j2π                              ⁡                                                              (                                                                  k                                  -                                  32                                                                )                                                                                      ⁢                            t                            ⁢                                                                                                                  ⁢                                                          Δ                              F                                                                                )                                                                    +                                              jexp                        ⁡                                                  (                                                                                    j2π                              ⁡                                                              (                                                                  k                                  +                                  32                                                                )                                                                                      ⁢                            t                            ⁢                                                                                                                  ⁢                                                          Δ                              F                                                                                )                                                                                      }                                                                                                                          =                            ⁢                                                [                                                            exp                      ⁡                                              (                                                                              -                                                          j64πΔ                              F                                                                                ⁢                          t                                                )                                                              +                                          jexp                      ⁡                                              (                                                                              j64πΔ                            F                                                    ⁢                          t                                                )                                                                              ]                                ⁢                                                      ∑                                          k                      =                                              -                        26                                                              26                                    ⁢                                                                          ⁢                                                            S                      k                                        ⁢                                          exp                      ⁡                                              (                                                  j2π                          ⁢                                                                                                          ⁢                          kt                          ⁢                                                                                                          ⁢                                                      Δ                            F                                                                          )                                                                                                                                                                    =                            ⁢                                                [                                                            exp                      ⁡                                              (                                                                              -                            j                                                    ⁢                                                      π                            2                                                    ⁢                          Ft                                                )                                                              +                                          jexp                      ⁡                                              (                                                  j                          ⁢                                                      π                            2                                                    ⁢                          Ft                                                )                                                                              ]                                ⁢                                                      ∑                                          k                      =                                              -                        26                                                              26                                    ⁢                                                                          ⁢                                                            S                      k                                        ⁢                                          exp                      ⁡                                              (                                                  j2π                          ⁢                                                                                                          ⁢                          kt                          ⁢                                                                                                          ⁢                                                      Δ                            F                                                                          )                                                                                                                                                                    =                            ⁢                                                [                                                            exp                      ⁡                                              (                                                                              -                            j                                                    ⁢                                                      π                            2                                                    ⁢                          Ft                                                )                                                              +                                          jexp                      ⁡                                              (                                                  j                          ⁢                                                      π                            2                                                    ⁢                          Ft                                                )                                                                              ]                                ⁢                                                      r                                          20                      ⁢                                                                                          ⁢                      M                                                        ⁡                                      (                    t                    )                                                                                                          (        1        )            
In the above equations, F is 40 MHz, Sk is a complex number that represents the amplitude and phase of the of the kth sub-carrier in the frequency band of the transmitted “duplicate” data symbol and ΔF represents the frequency spacing between sub-carriers, whilst r20M(t) is a continuous time signal representing the “original” data symbol.
This can be further expressed as
                                                                                          r                                      20                    ⁢                                                                                  ⁢                    Mdup                                                  ⁡                                  (                  t                  )                                            =                            ⁢                                                [                                                            exp                      ⁡                                              (                                                                              -                            j                                                    ⁢                                                      π                            2                                                    ⁢                          Ft                                                )                                                              +                                          jexp                      ⁡                                              (                                                  j                          ⁢                                                      π                            2                                                    ⁢                          Ft                                                )                                                                              ]                                ⁢                                                      r                                          20                      ⁢                                                                                          ⁢                      M                                                        ⁡                                      (                    t                    )                                                                                                                          =                            ⁢                                                (                                      1                    +                    j                                    )                                *                                  (                                                            cos                      ⁡                                              (                                                                              π                            2                                                    ⁢                          Ft                                                )                                                              -                                          sin                      ⁡                                              (                                                                              π                            2                                                    ⁢                          Ft                                                )                                                                              )                                ⁢                                                      r                                          20                      ⁢                                                                                          ⁢                      M                                                        ⁡                                      (                    t                    )                                                                                                                          =                            ⁢                                                (                                      1                    +                    j                                    )                                ⁢                                  2                                ⁢                                  cos                  ⁡                                      (                                                                                            π                          2                                                ⁢                        Ft                                            +                                              π                        4                                                              )                                                  ⁢                                                      r                                          20                      ⁢                                                                                          ⁢                      M                                                        ⁡                                      (                    t                    )                                                                                                          (        2        )            
These equations are based on equations 20-60 and 20-61 on pages 302 and 303 respectively of IEEE standard 802.11n-2009, where for simplicity it has been assumed that the matrix Q is equal to 1 for a single spatial stream, and the time delays for OFDM symbols and the differences between data and pilot subcarriers are ignored. In equation 1 above the same notation Sk is used regardless of whether k is a data or pilot sub-carrier.
The mean power of r20Mdup(t) is
                              E          ⁡                      [                                                                                                r                                          20                      ⁢                                                                                          ⁢                      Mdup                                                        ⁡                                      (                    t                    )                                                                              2                        ]                          =                              E            ⁡                          [                                                                                                              1                      +                      j                                                                            2                                ⁢                2                ⁢                                                                  ⁢                                                      cos                    2                                    ⁡                                      (                                                                                            π                          2                                                ⁢                        Ft                                            +                                              π                        4                                                              )                                                  ⁢                                                                                                                        r                                                  20                          ⁢                                                                                                          ⁢                          M                                                                    ⁡                                              (                        t                        )                                                                                                  2                                            ]                                =                      2            ⁢                                                  ⁢                          E              ⁡                              [                                                                                                                        r                                                  20                          ⁢                                                                                                          ⁢                          M                                                                    ⁡                                              (                        t                        )                                                                                                  2                                ]                                                                        (        3        )            
The peaks of r20M(t) occasionally coincide with maxima in the expression
      q    ⁡          (      t      )        =            (              1        +        j            )        ⁢          2        ⁢                  cos        ⁡                  (                                                    π                2                            ⁢              Ft                        +                          π              4                                )                    .      
The maximum magnitude of q(t) is 2, i.e. max(|q(t)|)=2, so that when the peaks of r20M(t) coincide with the peaks in q(t) the amplitude of the peaks of r20Mdup(t) is twice the amplitude of the peaks of r20M(t). Hence the RMS value of r20Mdup(t) is greater than that of r20M(t) by a factor of √{square root over (2)}, whilst the peaks of r20Mdup(t) are twice the amplitude of r20M(t). In other words, the peak-to-mean amplitude ratio of r20Mdup(t) is √{square root over (2)} times (3 dB) greater than that of r20M(t). For 40 MHz HT-MF and HT-GF signals other than MCS32, the signals in the upper and lower 20 MHz bands are independent and as a result their peak to mean amplitude ratio is not increased in this way.
This problem occurs not only in duplicate mode modulation schemes under the IEEE standard 802.11n, but also in non-HT duplicate modes in the draft IEEE 802.11ac standard.